It can be done, but unless it's a link card (since our state's cards are crap and don't scan) or a team member's card, we won't do it, because it could be fraudulent.
But if you insist, just select credit or debit in the payment screen, type in the amount you want (or hit the k1 key for full amount) and then it will give you and option to type in the number. If it's not a Target card, I know the credit card will require a supervisor override. Not sure about the debit.
When hitting credit/debit on the register you will come up with a screen where there is a spot to type in the card number. It's generally frowned upon in the multiple stores I've been through but sometimes you just don't have a choice. If you feel uncomfortable at all just ask for an id to make sure they're the same person. Follow the prompt, it should ask you for the expiration after you type in the 16 digit account code. It's been a while since I've done a manual, but I believe it runs everything as credit so if they have a debit only card this could prove problematic.